JEE Advanced Mix Test 56

An air-filled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k is (answer in integer)

Two parallel identical plates carry equal and opposite charges having a uniform charge of 88.9 μC. Positive plate is fixed on the ceiling of a box and the negative plate has to be suspended. If the area of the plates is 6.35 sq. m and 'm' is the mass of the negative plate, then the value of m in kg, is

A solid sphere of radius R has a charge Q distributed in its volume with a charge density p = kr^a, where k and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times that at r = R, find the value of a.

A point source of light S is placed a distance 10 cm in front of the center of a mirror of width 20 cm suspended vertically on a wall. An insect walks with a speed 10 cm/s in front of the mirror along a line parallel to the mirror at a distance 20 cm from it as shown in the figure. Find the maximum time (in seconds) during which the insect can see the image of the source S in the mirror.

2.616 g of an element (M) is heated with NaOH and NaNO₃ to produce Na₂MO₂ and NH₃. Ammonia produced is absorbed in 100 mL of 1 N H₂SO₄. Excess of the acid is back titrated with NaOH solution and required 80 mL of 0.25 M NaOH solution up to the equivalence point. What is the mass (in ‘g’) of hydrogen gas produced when 20 moles of ‘M’ is treated with excess of NaOH?

[Atomic mass : Cr = 52; Zn = 65.4; Fe = 56; Cu = 63.5; Ni = 28; H = 1]

2.27 g of mercuric iodide is added into 100 mL, 0.2 M aqueous solution of KI. If KI is 90% dissociated and potassium tetraiodidomercurate(II) is 80% dissociated, then the osmotic pressure of this solution at 300 K is found to be ‘x’ atm. Calculate the value of ‘100x’ if R = 0.08 L atm mol^-1 K^-1. [Atomic mass : Hg = 200, I = 127]

[Assume volume of solution remains constant and formation constant of K₂ [HgI₄] is very large].

A new element X forms a compound with chlorine, which contains 0.6873 g of the element per gram of chlorine. Specific heat of the element is 0.05 cal/gK. If the formula of chlorine is XCl_v, then the value of v is

If 2 sin α sin β + 3 cos β + 5 cos α sin β = √38  ∀ α, β ∈ R, then |adj (adj A)| is equal to where 

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of n for which this is possible is